2) Alex is on a sled. Alex starts from rest at the top of a 10 m frictionless hi

Question

2) Alex is on a sled. Alex starts from rest at the top of a 10 m frictionless hill, goes down the hill and ends up stopped some distance from the bottom of the hill in a field. Assume that the flat field which starts at the base of the hill has a coefficient of friction of 0.30. For simplicity assume Alex and the sled are together one object. Also assume that the transition between hill and field is gradual enough that you do not need to worry about the “bump” Alex feels at the bottom of the hill. (Hint: Think about the work done by the hill and the work done by the field as separate work even though they are both “work done by the earth”) a) At the end of the ride how far is Alex in the field from the base of the hill?

Explanation / Answer

Using law of conservation of energy

energy at the top of the hill = energy at the bottom of the hill

m*g*h = 0.5*m*v^2

m is the mass of the alex and sled cancels on both sides

then

g*h = 0.5*v^2

v = sqrt(2*g*h) = sqrt(2*9.8*10) = 14 m/sec

Using work-energy theorem

Work done by the net force = change in kinetic energy

-fk*S = -0.5*m*v^2

fk is the kinetic frictional force = mu_k*m*g

then

-mu_k*m*g*S = -0.5*m*v^2

0.3*9.8*S = 0.5*14^2

S = 33.33 m

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